Abstract

A method for obtaining the average refractive indexes of a birefringent material in the terahertz region in a single measurement with a standard terahertz time-domain spectrometer is presented. The method is based on processing the frequency-domain interference between terahertz pulses and echoes through the Fourier transform of the terahertz spectrum. The technique also allows the determination of the optical axis orientation of the material by making two measurements with different angles of the sample optical axis.

© 2014 Optical Society of America

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  1. K. Wiesauer and C. Jördens, J. Infrared, Millimeter, Terahertz Waves 34, 663 (2013).
    [CrossRef]
  2. S. Ebara, Y. Hirota, M. Tani, and M. Hangyo, “Highly sensitive birefringence measurement in THz frequency region and its application to stress measurement,” presented at the Joint 32nd International Conference on Infrared and Millimeter Waves and 15th International Conference on Terahertz Electronics (IRMMW-THz), Cardiff, Wales, September2007.
  3. C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
    [CrossRef]
  4. C. Jördens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, Appl. Opt. 48, 2037 (2009).
    [CrossRef]
  5. Y. Kim, M. Yi, B. Kim, and J. Ahn, Appl. Opt. 50, 2906 (2011).
    [CrossRef]
  6. M. Reid and R. Fedosejevs, Appl. Opt. 45, 2766 (2006).
    [CrossRef]
  7. S. Katletz, M. Pfleger, H. Uhringer, M. Mikulics, N. Vieweg, O. Peters, B. Scherger, M. Scheller, M. Koch, and K. Wiesauer, Opt. Express 20, 23025 (2012).
    [CrossRef]
  8. L. Duvillaret, F. Garet, and J. L. Coutaz, J. Opt. Soc. Am. B 17, 452 (2000).
    [CrossRef]
  9. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990).
    [CrossRef]

2013 (1)

K. Wiesauer and C. Jördens, J. Infrared, Millimeter, Terahertz Waves 34, 663 (2013).
[CrossRef]

2012 (1)

2011 (1)

2010 (1)

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
[CrossRef]

2009 (1)

2006 (1)

2000 (1)

1990 (1)

Ahn, J.

Coutaz, J. L.

Duvillaret, L.

Ebara, S.

S. Ebara, Y. Hirota, M. Tani, and M. Hangyo, “Highly sensitive birefringence measurement in THz frequency region and its application to stress measurement,” presented at the Joint 32nd International Conference on Infrared and Millimeter Waves and 15th International Conference on Terahertz Electronics (IRMMW-THz), Cardiff, Wales, September2007.

Fattinger, C.

Fedosejevs, R.

Garet, F.

Grischkowsky, D.

Hangyo, M.

S. Ebara, Y. Hirota, M. Tani, and M. Hangyo, “Highly sensitive birefringence measurement in THz frequency region and its application to stress measurement,” presented at the Joint 32nd International Conference on Infrared and Millimeter Waves and 15th International Conference on Terahertz Electronics (IRMMW-THz), Cardiff, Wales, September2007.

Hirota, Y.

S. Ebara, Y. Hirota, M. Tani, and M. Hangyo, “Highly sensitive birefringence measurement in THz frequency region and its application to stress measurement,” presented at the Joint 32nd International Conference on Infrared and Millimeter Waves and 15th International Conference on Terahertz Electronics (IRMMW-THz), Cardiff, Wales, September2007.

Jansen, C.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
[CrossRef]

Jördens, C.

K. Wiesauer and C. Jördens, J. Infrared, Millimeter, Terahertz Waves 34, 663 (2013).
[CrossRef]

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
[CrossRef]

C. Jördens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, Appl. Opt. 48, 2037 (2009).
[CrossRef]

Katletz, S.

Keiding, S.

Kim, B.

Kim, Y.

Koch, M.

Mikulics, M.

Peters, O.

Pfleger, M.

Reid, M.

Reisecker, V.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
[CrossRef]

Romeike, D.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
[CrossRef]

Scheller, M.

Scherger, B.

Tani, M.

S. Ebara, Y. Hirota, M. Tani, and M. Hangyo, “Highly sensitive birefringence measurement in THz frequency region and its application to stress measurement,” presented at the Joint 32nd International Conference on Infrared and Millimeter Waves and 15th International Conference on Terahertz Electronics (IRMMW-THz), Cardiff, Wales, September2007.

Uhringer, H.

van Exter, M.

Vieweg, N.

Wichmann, M.

Wiesauer, K.

K. Wiesauer and C. Jördens, J. Infrared, Millimeter, Terahertz Waves 34, 663 (2013).
[CrossRef]

S. Katletz, M. Pfleger, H. Uhringer, M. Mikulics, N. Vieweg, O. Peters, B. Scherger, M. Scheller, M. Koch, and K. Wiesauer, Opt. Express 20, 23025 (2012).
[CrossRef]

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
[CrossRef]

C. Jördens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, Appl. Opt. 48, 2037 (2009).
[CrossRef]

Wietzke, S.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
[CrossRef]

Yi, M.

Zentgraf, T.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
[CrossRef]

Appl. Opt. (3)

Compos. Sci. Technol. (1)

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, V. Reisecker, and M. Koch, Compos. Sci. Technol. 70, 472(2010).
[CrossRef]

J. Infrared, Millimeter, Terahertz Waves (1)

K. Wiesauer and C. Jördens, J. Infrared, Millimeter, Terahertz Waves 34, 663 (2013).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (1)

Other (1)

S. Ebara, Y. Hirota, M. Tani, and M. Hangyo, “Highly sensitive birefringence measurement in THz frequency region and its application to stress measurement,” presented at the Joint 32nd International Conference on Infrared and Millimeter Waves and 15th International Conference on Terahertz Electronics (IRMMW-THz), Cardiff, Wales, September2007.

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Figures (6)

Fig. 1.
Fig. 1.

Projection of a terahertz electric field onto a birefringent material.

Fig. 2.
Fig. 2.

Numerical simulation of the DFT applied to the frequency-domain signal of Eq. (2).

Fig. 3.
Fig. 3.

Numerical simulation of the DFT applied to the frequency-domain signal [Eq. (2)].

Fig. 4.
Fig. 4.

Terahertz TDS spectrometer setup.

Fig. 5.
Fig. 5.

(a) Temporal measurement of the terahertz spectrometer with a sapphire window of 1 mm and (b) modulus of the DFT applied to the signal in (a). (c) Squared modulus of the DFT applied to the signal in (b).

Fig. 6.
Fig. 6.

Change in the DFT of the modulus of the terahertz spectrum when the sapphire sample mount is rotated in 5° steps.

Equations (8)

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ET(ω)=|Ei(ω)|cos2(θ)ejφi(ω)To(ω)Go(ω,d)m=0+(ro(ω)Go2(ω,d))m+|Ei(ω)|sin2(θ)ejφi(ω)Te(ω)Ge(ω,d)m=0+(re(ω)Ge2(ω,d))m,
|ET(ω)|2=a1(θ,ne,no)|Ei(ω)|2cos((none)ωdc)+a2(θ,ne,no)|Ei(ω)|2cos((3none)ωdc)+a3(θ,ne,no)|Ei(ω)|2cos((no3ne)ωdc)+a4(θ,ne,no)|Ei(ω)|2cos(2noωdc)+a5(θ,ne,no)|Ei(ω)|2cos(2neωdc)+a6(θ,ne,no)|Ei(ω)|2cos(3(none)ωdc)+a7(θ,ne,no)|Ei(ω)|2.
YT(t)=H1(θ,ne,no)δ(t|none|dc)+H2(θ,ne,no)δ(t|3none|dc)+H3(θ,ne,no)δ(t|no3ne|dc)+H4(θ,ne,no)δ(t2nodc)+H5(θ,ne,no)δ(t2nedc)+H6(θ,ne,no)δ(t3|none|dc)+H7(θ,ne,no)δ(0).
En=T2dmEc+c2dmET+cT2d2mEd,
H4H5=tg4θ(4ne(ne+1)2)2(ne1)2(ne+1)2(4no(no+1)2)2(no1)2(no+1)2,
θtg1((H4H5)1/4).
H4+H2H5+H3=tg2θf(no,ne,θ),
θtg1(H4+H2H5+H3)1/2,

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